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Understanding Quadratic Equations: Square Roots and Areas

Learn to solve quadratic equations by finding square roots, understand the concept of square roots, solve equations using square roots, identify perfect squares, and find the area of figures. Homework includes practicing multiples of 4 and applying the concepts learned.

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Understanding Quadratic Equations: Square Roots and Areas

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  1. Do Now 4/19/10 • Copy HW in your planner. • Text p. 655, #4-48 multiples of 4, #56 & 60 A= 36 A = 6² A= 16 What is the area for each figure? A = 4² • What are the dimensions for each figure? 6 4 • Write an equation for area of the figure? • Can you think of an equation • for ONE side of the figure? 4 6

  2. Objective • SWBAT solve quadratic equations by finding square roots

  3. Remember This???Section 2.7 “Find Square Roots and Compare Numbers” If b² = a then b is the square root of a. TheSQUARE ROOTof a number is denoted by the symbol , which is called aradical. radicand

  4. Square Roots • All positive real numbers have two square roots, a positive and negative square root. • The symbol is read as “plus or minus” and refers to both the positive and negative square root. • Negative real numbers do not have real square roots. So there is no solution. no solution The square of an integer is called a perfect square.

  5. Not PERFECT??? The square root of a whole number that is NOT a perfect square is an IRRATIONAL NUMBER. numbers that cannot be written as a quotient (fraction, ratio) of two integers and the decimal neither terminates nor repeats. To find the square root of a number that is not a perfect square estimate or use a calculator to find the square root.

  6. Section 10.4 “Use Square Roots to Solve Quadratic Equations” • To use square roots to solve a quadratic equation of the form ax² + bx + c = 0, first isolate x² on one side of the equation to obtain x² = d. Examples Solving x² = d by Taking Square Roots - If d > 0, then x² = d has two solutions: - If d = 0, then x² = d has one solution: - If d < 0, then x² = d has no solution: no solution no solution

  7. Try It Out… No solution

  8. Take square roots of a fraction • In cases where you need to take the square root of a fraction whose numerator and denominator are perfect squares, the radical can be written as a fraction. • For example, can be written as .

  9. Try It Out…

  10. Solve the quadratic equation. Round your answer to the nearest hundredth.

  11. HomeworkText p. 655, #4-48 multiples of 4, #56 & 60

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